A variational model for swirling flow states with stagnant region

We introduce a variational formulation for computing swirling flow states with stagnant regions in a pipe. The new extended flow force functional is maximized with respect to the location of the stagnant region boundary, leading to a swirling flow state with minimum swirl number. By allowing a jump in velocity across the vortex sheet that bounds the stagnant region, while the static pressure remains continuous, our variational principle does not require anymore additional kinematic conditions such as vanishing velocity. Solutions with or without velocity jump are naturally recovered. An assessment of the proposed model against experimental data is also presented.